Mach principle, 2

However, general relativity predicts and experiments confirm that gravitational waves do exist: the relevant observations were awarded by the 1993 physics Nobel prize, too. The waves are vibrations of the space itself. It means that the metric tensor remembers the information about the geometry – and curvature at each point, even in the empty space, something that Mach’s principle specifically wanted to prohibit.

Einstein had thought that Mach’s Principle was the way to go because it (also) made the universality encoded in the equivalence principle manifest. The equivalence principle says that all objects will be influenced equally – the same acceleration – by the whatever agent is causing gravity. Mach’s principle satisfies the criterion “totally” – it removes any field-like agent. Well, it’s going “too far” in this sense. Of course that Einstein was struggling for years to make Mach’s Principle compatible with the speed limit c – and GR is what eventually came out of it.

– Lubos Motl

2014.06.29 Sunday ACHK

Open Source MindOS

這段改編自 2010 年 4 月 10 日的對話。

(安:我發覺我都有一個,大部人也沒有的優點。我這類性格的人,又真的很少。)

什麼優點?

(安:我比較容易受教。我舉一個例子:

有一次,我和朋友甲討論一個邏輯問題。我的心目中一直以為,因為「先決條件」和「充份條件」,是兩個不同的概念,所以沒有關係。但是,甲指出「充份條件」其實即是,「所有先決條件」的總和。

經過他的解釋,我發覺原本「兩者沒有關係」的想法是錯的。我就自然立刻承認。我不單不會因為發現自己錯,有絲毫不高興;我反而會十分開心,因為,「發現自己原本錯」,其實就即是「發現了真正的答案」。

換句話說,「發現自己錯」的那一刻,正正是我知識增長,和智力提升的那一刻。)

那就即是話,你腦中的作業系統,是 Open Source 的 —— 容許別人修改。

(安:但是,我發覺大部分人,也不是那樣的。他們不單不會因為,發現「真正答案」而高興,甚至會全盤否定它,為的只是要「自己不會錯」。

這是我不能理解的。直到學到你的「心靈作業系統」理論,加上哲學家羅素的那一句,我才開始理解到,為何大部地球人,無論在過去、現在、將來,也「不可能有錯」。)

— Me@2014.06.26

A stupid man’s report of what a clever man says is never accurate, because he unconsciously translates what he hears into something that he can understand.

— A History of Western Philosophy

— Bertrand Russell

2014.06.27 Friday (c) All rights reserved by ACHK

Craftsmanship

mantrax5 2 hours ago | link

“You know, one of the things that really hurt Apple was after I left John Sculley got a very serious disease. It’s the disease of thinking that a really great idea is 90% of the work. And if you just tell all these other people “here’s this great idea,” then of course they can go off and make it happen.

And the problem with that is that there’s just a tremendous amount of craftsmanship in between a great idea and a great product. And as you evolve that great idea, it changes and grows. It never comes out like it starts because you learn a lot more as you get into the subtleties of it. And you also find there are tremendous tradeoffs that you have to make. There are just certain things you can’t make electrons do. There are certain things you can’t make plastic do. Or glass do. Or factories do. Or robots do.

Designing a product is keeping five thousand things in your brain and fitting them all together in new and different ways to get what you want. And every day you discover something new that is a new problem or a new opportunity to fit these things together a little differently.

And it’s that process that is the magic.”

~ Steve Jobs

This is why Apple doesn’t make “vision” videos now, and it didn’t during the Jobs years. During the period they did, they had serious problems in shipping any of the visions they have shown the world.

Microsoft is a bit like that. They know where the world is going, and Bill Gates himself knew from the very start where the world is going (short of a brief period where he conveniently ignored the Internet will happen). But they thought the fact they knew, that they had this cool idea and projection of how things will happen was giving them enough advantage. Nope.

It’s risk-free to ship vision videos. They’re like free T-shirts. There’s infinite demand. But when it comes to shipping products based on them, most people can’t live with the compromises and risk-taking a real product requires in order to ship.

With a new product you can’t just look at the competition and confirm that what you have will work. You’re on your own. Do you have the guts?

— Hacker News

2014.06.24 Tuesday ACHK

The Lucifer Effect

Stanford prison experiment

Zimbardo’s book, The Lucifer Effect, gets its title from the metamorphosis of Lucifer into Satan. Though the Christian Scriptures do not make this claim, according to Christian legend, Lucifer was once God’s favorite angel until he challenged God’s authority and was cast into Hell with all the other fallen angels. Thus, Zimbardo derives this title to explain how good people turn evil. Zimbardo’s main assumption on why good people do awful things is due to situational influences and power given from authority.

The Lucifer Effect was written in response to his findings in the Stanford Prison Experiment. Zimbardo believes that personality characteristics could play a role in how violent or submissive actions are manifested. In the book, Zimbardo says that humans cannot be defined as “good” or “evil” because we have the ability to act as both especially at the hand of the situation. According to Zimbardo, “Good people can be induced, seduced, and initiated into behaving in evil ways. They can also be led to act in irrational, stupid, self-destructive, antisocial, and mindless ways when they are immersed in ‘total situations’ that impact human nature in ways that challenge our sense of the stability and consistency of individual personality, of character, and of morality.”

He also notes that we as humans wish to believe in unchanging goodness of people and our power to resist situational and external pressures and temptations. In chapter 12, “Investigating Social Dynamics: Power, Conformity, and Obedience”, Zimbardo discusses that peer pressure, the desire to be ‘cool’, the fear of rejection, and simply being a part of a group are the focal points to acting preposterous to your character.

In The Journal of the American Medical Association, Zimbardo’s situational perspective received support from other social situational experiments that demonstrated the same idea and concept. Almost ten years prior to the Stanford Prison Experiment (1971), Stanley Milgram conducted research on obedient behavior in 1965 that embraced situational forces. Milgram had “teachers” that delivered mock electric shocks to the “learner” for every wrong answer that was given in a multiple choice test. The teachers however did not know that the electric shocks weren’t real but still continued to deliver them to the learner. At the end of the experiment, 65% of men ages 20–50 complied fully up to the very last voltage. In the same room as the teacher, there was a “confederate” that kept tabs on the teacher and if they were delivering the shocks to each wrong answer. In the beginning of the study, participants signed a waiver that clearly explained the ability to opt-out of the experiment and not deliver the shocks. But with the surprising result rate of teachers who did continue to shock the learners, there was a situational force. The situational force that influenced the teachers to continue was the voice of the confederate egging them on by phrases such as, “I advise you to continue with this experiment” or “I am telling you to continue delivering the shocks” and the one that caught most teachers was “You must continue with the shocks.” Although the teachers knew that they could leave the experiment at any point in time, they still continued when they felt uncomfortable because of the confederate’s voice demanding to proceed.

Both Milgram and Zimbardo’s experiment tested situational forces on an individual. Both results concluded that irrational behavior compared to one’s character is plausible for any human because we have both tendencies in our nature.

— Wikipedia on Philip Zimbardo

2014.06.23 Monday ACHK

點石不成金

這段改編自 2010 年 4 月 10 日的對話。

我發現我有一個,一般人沒有的優點,就是除了想自己才智過人外,亦同時想令到身邊的人,有我的才智,或者有超過我的才智。

(安:我都有一點兒這個傾向。但是,最大的問題是,我發覺大部分人,也是不能提升的。例如,我試過以一個免費補習的形式,教導一位舊同事英文文法。那樣,他就可以有系統地,學習英文文法。

我不是說我是英文文法專家,但我純熟過他很多,所以,我教他的文法,一定足夠他平日工作使用。

不過,在上了很多課之後,我發現他仍然會問我一大堆,在課程之中,明明已經教過他的東西。換句話之,我花了那麼多時間後,他竟然可以近乎一句不漏地,把我教的內容忘記。)

有些情況下,應該幫助別人。有些情況下,則不應該幫助別人。至於哪些情況下應該幫,哪些情況下不應幫,可根據一個大原則,就是

如果你幫他,事情的發展是好還是壞?

換而言之,你要企圖做好事,但千萬不要企圖做好人。時刻「企圖做好人」的危機是,你很多時會「好心做壞事」,害了別人,又害了自己。

你在這件事上,棋差一着的地方是,你竟然「免費」教導他。沒有成本,自然不會上心。毋須付出,自然不會重視。

如果他有交學費,而那些學費是來自他自己,不是來自他父母金錢的話,他就不會對你的教導,左耳入右耳出。

— Me@2014.06.23

If you’re good at something, never do it for free.

— The Dark Knight

When you give a lot of importance to someone in your life, you lose your importance in their life.

2014.06.23 Monday (c) All rights reserved by ACHK

Mach principle

In theoretical physics, particularly in discussions of gravitation theories, a Mach principle is any of a class of principles which are more specific statements of Mach’s principle.

The broad notion is that “mass there influences inertia here”. Any statement which — though possibly far more specific than this — follows in this spirit may be classified as a “Mach principle”. The truth of these statements depends on the particular statement. (The truth also depends on the theory of gravity, though Einstein’s general relativity is the most frequently discussed theory.)

Examples

Hermann Bondi and Joseph Samuel have listed eleven distinct statements which can be called Mach principles, labelled by Mach0 through Mach10. Though their list is not necessarily exhaustive, it does give a flavor for the variety possible.

  • Mach0: The universe, as represented by the average motion of distant galaxies, does not appear to rotate relative to local inertial frames.
  • Mach1: Newton’s gravitational constant G is a dynamical field.
  • Mach2: An isolated body in otherwise empty space has no inertia.
  • Mach3: Local inertial frames are affected by the cosmic motion and distribution of matter.
  • Mach4: The universe is spatially closed.
  • Mach5: The total energy, angular and linear momentum of the universe are zero.
  • Mach6: Inertial mass is affected by the global distribution of matter.
  • Mach7: If you take away all matter, there is no more space.
  • Mach8: ( \Omega \ \stackrel{\mathrm{def}}{=}\ 4 \pi \rho G T^2 ) is a definite number, of order unity, where ( \rho ) is the mean density of matter in the universe, and T is the Hubble time.
  • Mach9: The theory contains no absolute elements.
  • Mach10: Overall rigid rotations and translations of a system are unobservable.

— Wikipedia on Mach principle

2014.06.22 Sunday ACHK

The Nice Guy Paradox, 2

Being a nice guy can be a problem, because “always being nice” gives no feedback and no directions. In effect, “always being nice” gives people an infinite number of choices. Remember,

choices ~ headaches

In other words, you should be nice as often as possible, but not always. Be angry when you have to.

— Me@2011.06.26

— Me@2014.06.22

2014.06.22 Sunday (c) All rights reserved by ACHK

Memory 5.4

這段改編自 2010 年 7 月 29 日的對話。

.

(HSY:會考剛放榜,我的物理成績只有 C。所以,學校當局很可能會,不容許我選修高考物理,而要我改為選修,例如,「數學與統計」科。

現在,我要去和負責相關事項的老師,討論這個問題。那樣,我應該要講些什麼,才可以有機會說服到他,給我選修物理呢?)

你試試這樣:

在對話中,你要不斷重複著,同一個意思,以示你有無比的決心,去讀好物理科;但是,你又千萬不要,明顯地重複著,同一個說話,以免對方覺得你,沒有禮貌。

換句話說,你要用無限句不同的說話,去表達同一個意思,例如:

甲 = 你

乙 = 對方

乙:…

甲:我其實很喜歡物理。

乙:…

甲:我真的很喜歡物理。

乙:…

甲:你講得很有道理,不過,我對物理的信心,大過數學很多。

乙:…

甲:但是,我讀的數學天份,沒有物理那麼高。

乙:…

甲:我也有考慮這一點,但是,我如果讀物理,我的父母會安心一點。

乙:…

甲:讀物理的話,我奪得好成績的機會,會大很多。

乙:…

甲:…

— Me@2014.06.20

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2014.06.21 Saturday (c) All rights reserved by ACHK

Charge, 2

Charge (physics), the susceptibility of a body to one of the fundamental forces

  • Color charge, a property of quarks and gluons, related to their strong interactions
  • Electric charge, a property which determines the electromagnetic interaction of subatomic particles
  • Magnetic charge, a property of theoretical magnetic monopoles

— Wikipedia on Charge

Symmetry and conservation

Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate quantity to momentum). That is, conservation of momentum is a consequence of the fact that the laws of physics do not depend on position; this is a special case of Noether’s theorem.

— Wikipedia on Momentum

Momentum is the Noether charge of translational invariance. As such, even fields as well as other things can have momentum, not just particles. However, in curved spacetime which isn’t asymptotically Minkowski, momentum isn’t defined at all.

2014.06.19 Thursday ACHK

點石成金

這段改編自 2010 年 4 月 10 日的對話。

(安:最近,我們才有稍為詳細的對話。在和你對話之前,我一路不知道,在很多情境之下,我自己其實沒有問題。問題在於其他人。)

什麼情境?

(安:在工作環境中,有時需要解釋一些東西予同事聽。一部分情況下,當我耐心地講完後,那位同事竟然一句也不明白,半句也不同意。那樣,我就覺得很震撼:「我明明是講得很詳細和清晰,為什麼他接收不到呢?」

該同事會直情會去到一個地步,覺得自己在任何情況下,也不可能有錯,亦不可能有東西不知道。

然後,我又會很自責:「會不會是我自以為詳細清晰,實質表達欠佳?」

直到最近和你對話,你提醒了我,其實這個星球,是一個精神病院,我才發覺,根本大部分地球人,都是愚中帶蠢的,我才不再那麼內疚,因為,大部分人聽不明白我的說話,未必是我的錯。)

對於初中或以下的人而言,大部分是可教的。對於高中或以上的人來說,大部分也是不可教的。你是例外,因為你以這個年紀,竟然仍會接受,別人的教導。

面對一些可教的人,我有「點石成金」的教學功力。「點石成金」在這裡的意思是,以一夕話的時間,解決你起碼一個知識的障礙,或者長久的心結。

如果我開一間補習社,它的名字將會是,「點石成金補習社」。

— Me@2014.06.17

2014.06.18 Wednesday (c) All rights reserved by ACHK

Time Reversal 2

Lessons from the Light, 5.3

They found that T is indeed violated.

All perfectly fine and glorious. The pet peeve only comes up in the sub-headline of the SLAC press release: “Time’s quantum arrow has a preferred direction, new analysis shows.” Colorful language rather than precise statement, to be sure, but colorful language that is extremely misleading.

“Time’s arrow,” in the sense that the phrase is conventionally used (by the kind of folks who would conventionally use such a phrase), refers to the myriad ways in which the past is different from the future in our macroscopic experiential reality. Entropy increases with time; … This new measurement in the B meson system — indeed, the entire phenomenon of T violation — has absolutely nothing to do with that arrow of time.

The reason is pretty simple to understand. The arrow of time centers on the concept of irreversibility — things happen in one direction of time but not the other. You can scramble eggs, but not unscramble them, etc. That’s not at all what’s going on in the B mesons. The oscillations between different types of meson happen perfectly well in both directions of time, just with ever-so-slightly different rates.

The particle-physics processes in question, in other words, are perfectly reversible. Information is not lost over time; you can figure out exactly what the quantum state used to be by knowing what it is now. (It’s “unitary,” to use the jargon word.) That’s utterly different from the macroscopic arrow of time.

— Time-Reversal Violation Is Not the “Arrow of Time”

— Sean Carroll

2014.06.13 Friday ACHK

The paradox of happiness solved

It is often said that we fail to attain pleasures if we deliberately seek them. This has been described variously, by many:

    Viktor Frankl in Man’s Search for Meaning:

    Happiness cannot be pursued; it must ensue, and it only does so as the unintended side effect of one’s personal dedication to a cause greater than oneself …

— Wikipedia on Paradox of hedonism

The paradox of happiness: 

If you do good work, you will feel happy.

However, if you do good work only because of the desire of getting happiness, you will not get it.

[selfless]

happiness ~ progress ~ self transcendence

do good work ~ keep going to the next levels

[selfish]

seeking happiness directly ~ focus on oneself ~ trapped at the same level

no progress ~ unhappiness

— Me@2011.06.22

快樂

~ 快

快樂源於進步快。

— Me@2014.06.13

2014.06.13 Friday (c) All rights reserved by ACHK

功夫傻瓜 3

中學實驗報告 4

這段改編自 2010 年 7 月 29 日的對話。

每次我介紹「魔法時間表」時,通常,學生也會說執行不到,因為有很多功課。例如,根據「魔法時間表」的設計,今天應該花三小時,去溫習物理科。但是,物理老師卻給了一份功課,花了你兩個多小時,才可以完成。餘下自然沒有什麼時間,可以用來溫習。

我的回應是,「做功課」就即是「做練習」。你試想想,如果「做練習」也不算是「溫習」,那怎樣才算是「溫習」呢?

(CPK:閱讀課文?)

閱讀了課文後,你又怎樣知道,自己是不是真的熟習內容,考試時奪不奪到分數?

(CPK:試一試做類似考試的題目。)

那不就是「做功課」嗎?

所以,如果你做了兩小時的物理功課,其實就即是完成了,兩小時的物理溫習。「功課」並不會阻礙你時間表的進展,因為「功課」根本就是,你編時間表時,原訂「溫習」的一部分。「練習」不單是「溫習」的一部分,它更加是「溫習」之中,最重要的那部分,因為「練習」就是,把「知識」化成行動。

一般人也不覺得「做功課」就是「溫習」,主要的原因是,他們平時「做功課」的主要目的,就只是「交功課」。他們不會追究,如何從一份功課中,學得最多的學術知識,奪取最多的考試分數。那是病態版本的「只問付出,不問收穫」。那是十分不負責任的表現。

正確的態度是,一邊做功課,一邊製作我之前所講的「魔法筆記」。亦即是話,做功課時,你要有意識地偵測,當中哪些內容,有需要記得,而自己又有機會不記得。然後,把它們歸納於,該科的「魔法筆記」之中。

(CPK:但是,有些功課的題目,實在和考試的內容和形式,十分不類似,做來也沒有用。)

我上次不是詳細地教過你們,應付無謂的功課時,如何盡量減輕損失嗎?

— Me@2014.06.11

2014.06.12 Thursday (c) All rights reserved by ACHK

Time Reversal

Lessons from the Light, 5.2

Note that among C, P, T, only T is an “antilinear operator” which means that

T | \lambda \psi \rangle = \lambda* T | \psi \rangle

including the asterisk which means complex conjugation (that’s the reason of the prefix, anti-). Various combinations of C, P, T are linear or antilinear depending on whether T is included.

Note that the complex conjugation is needed for the time reversal already in ordinary non-relativistic quantum mechanics because the complex conjugation is the only sensible way to change ( \exp(+ipx/\hbar) ) to ( \exp(-ipx/\hbar) ), i.e. to change the sign of the momentum p – and the velocity v = dx/dt – which is needed for particles to evolve backwards.

— BaBar directly measures time reversal violation

— Lubos Motl

2014.06.11 Wednesday ACHK

Confusion

Presentation 基本原理 2

con

~ fuse

~ draw together

confuse ~ con + fuse

To avoid confusion, say only one point at a time. Don’t try to fuse several ideas at the same time, intentionally or unintentionally. In other words, present ideas in series, not in parallel.

— Me@2013-10-23 01:48:22 PM

The German philosopher G. W. F. Hegel wrote that any philosopher who uses the word “and” too often cannot be a good philosopher.

— Advice for the Young Scientist

— John Baez

2014.06.05 Thursday (c) All rights reserved by ACHK

長頸豹 3

尋找時間的定義 1.2

SICM, 3.2 | SICP, 2.2

這段改編自 2010 年 4 月 10 日的對話。

涉獵多門知識,即使對於「本行」的發展,也會有意想不到的幫助。

例如,我對「什麼是時間」這個物理問題,有極之大的興趣。我想像,如果我只閱讀和研究物理,可能窮一身的時間,也沒有寸進。

估不到,在大概 2006 年,我從一本電腦界的神作中,得到了靈感,開始對「時間定義」有一點理解。然後在今年(2010),再加上我在大學時代時,長期訓練得來的「語理分析」功力,我破解了,「時間」的大部分意思。

(安:你上星期也有提及過,那本電腦界的神作。)

又例如,如果一個人過身後,仍然以某種形式存在的話,究竟確實是以哪一種,或者怎麼樣的形式來存在呢?

從物理和電腦知識中,我得到了一些關鍵靈感。

「靈感」中的「靈」,其實就是解「靈活」、「靈通」,即是有大量和多類型的資料或消息來源。

— Me@2014.06.03

2014.06.03 Tuesday (c) All rights reserved by ACHK

99% is no real certainty

Dear Giotis, they were formally at least 99.9999999% certain, that’s what the 6-7 sigma confidence level means, and even when some possible “qualitatively different errors” are considered as possibilities, their certainty is still vastly higher than 99%.

As I wrote in an update, Pryke of BICEP2 says that the rumors about the planned retractions by BICEP are pure bullshit.

99% is no real certainty. It’s just a laymen’s myth that 99% is high enough to treat something as a certainty. It’s less than 2 sigma. In hard sciences, if something comes out to confirm a theory at a 99% level, a scientist doesn’t consider it even as significant evidence to be carefully studied!

— Lubos Motl

This file is licensed under the Creative Commons Attribution 2.5 Generic license. Author: Mwtoews

In statistics, the 68–95–99.7 rule, also known as the three-sigma rule or empirical rule, states that nearly all values lie within three standard deviations of the mean in a normal distribution.

68.27% of the values lie within one standard deviation of the mean. Similarly, 95.45% of the values lie within two standard deviations of the mean. Nearly all (99.73%) of the values lie within three standard deviations of the mean.

— Wikipedia on 68–95–99.7 rule

2014.06.03 Tuesday ACHK

The Magic City

.

The second theme is concerned explicitly with technology. It is a law of life in the magic city that if you wish for anything you can have it. But with this law goes a special rule about machines. If anyone wishes for a piece of machinery, he is compelled to keep it and go on using it for the rest of his life.

– Disturbing the Universe, p.4

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.

.

2009.12.21 Monday ACHK